Oil or gas wells are often surveyed to determine one or more geological, petrophysical, geophysical, and well production properties (“parameters of interest”) using electronic measuring instruments conveyed into the borehole by an umbilical such as a cable, a wireline, slickline, drill pipe or coiled tubing. Tools adapted to perform such surveys are commonly referred to as formation evaluation (FE) tools. These tools use electrical, acoustical, nuclear and/or magnetic energy to stimulate the formations and fluids within the borehole and measure the response of the formations and fluids. The measurements made by downhole instruments are transmitted back to the surface.
In order to reduce the amount of rig time needed for wireline logging, it is common practice to run multiple sensors in a single run. FOCUS™, from Baker Atlas Inc., is a high efficiency premium open hole logging system. All of the downhole instruments have been redesigned, incorporating advanced downhole sensor technology, into shorter, lighter, more reliable logging instruments, capable of providing formation evaluation measurements with the same precision and accuracy as the industry's highest quality sensors, at much higher logging speeds. Logging speeds are up to twice the speed of conventional triple-combo and quad combo logging tool strings. Speeds of up to 3600 ft/hr (1080 m/min) are possible. The logging system may include four standard major open-hole measurements (resistivity, density, neutron, acoustic) plus auxiliary services.
Some petrophysical properties are easily obtained from downhole FE measurements. These include porosity, bulk density, NMR relaxation T1 and T2 spectra, and compressional and shear wave velocities. Other petrophysical properties that are of importance in reservoir evaluation and development are difficult if not impossible to measure. Properties that are difficult or impossible to measure include, for example permeability, relative permeability, resistivity formation factor, capillary pressure, and NMR surface relaxivity. These are typically derived from correlations or petrophysical relationships.
One of the problems with relating the different petrophysical properties of an earth formation to each other is that they are all macroscopically measured quantities that depend ultimately on the microscopic arrangement of the constituents of the earth formation. An early attempt at predicting macroscopic properties based on microscopic models is due to Gassmann (1951) in which the earth formation is modeled as a hexagonal close packing of equal-sized elastic spheres. Based on this simplistic model, it is possible to predict the stress dependence of the packing in terms of the moduli of the constituent spheres.
The earth, of course, is not made out of a hexagonal close packing of equal-size elastic spheres. Finney (1968) measured the spatial coordinates of some 8000 spheres in a random packing of spheres, thereby completely determining the geometry of the microstructure of the packing. This packing may be regarded as a physical model of a clean sediment of well-sorted sand grains. The term “sorting” refers to the distribution of grain sizes: a poorly sorted sandstone has a large range of grain sizes while a well sorted sandstone has grains of substantially the same size. Such sediments can be deposited in a wide spectrum of depositional environments, from nonmarine to basinal deep water. The model developed by Finney is primarily applicable to earth formations comprised of compacted clastic sediments. The term “clastic” refers to rocks made up of fragments of preexisting rocks. Based on the model of Finney, there have been numerous papers that discuss the prediction of formation properties. For example, Bryant and Raikes (1995) used the central core of 3367 spheres in Finney's pack, which has a porosity of 36.2% to try to predict elastic wave velocities in sandstones. In Toumelin et al. (2004), the NMR response of porous rocks was simulated using a continuous, three-dimensional (3D) random-walk algorithm. Diffusion pathways of individual fluid molecules are determined within the 3-D porous model. The method of Toumelin allows the rigorous treatment of T1 and T2 relaxation times with a minimum of assumptions and for arbitrary pulse sequences. Toumelin also discusses the numerical accuracy of the simulation. The results reproduce NMR decay and build-up while accounting for restricted diffusion in porous media, fluid wettabilities, and fluid spatial distributions.
U.S. patent application Ser. No. 11/146,886, now U.S. patent Ser. No. 7,356,413 to Georgi and having the same assignee as the present disclosure discloses adjusting parameters of a pore-scale geometric model of a clastic earth formation so that the output of the model matches measurements made on a core sample. Additional properties of the earth formation are predicted using the pore-scale model. The additional properties may be based on additional measurements of properties of a fluid in the formation.
U.S. Pat. No. 7,257,490 to Georgi et al., having the same assignee as the present disclosure discloses a method of evaluating an earth formation containing clastic sediments. At least one formation evaluation sensor is conveyed in a borehole in the earth formation and a measurement is made of a property of the earth formation. A pore-scale model of the earth formation whose output substantially matches a value of the measurement is defined. The pore scale model includes grains of the clastic material. The pore scale model is then used to estimate a value of an additional property of the earth formation.
U.S. patent application Ser. No. 11/445,023 of Georgi et al., now U.S. patent Ser. No. 7,363,161, having the same assignee as the present disclosure, discloses a method of evaluating an earth formation containing clastics. NMR signals indicative of a property of the earth formation are obtained. A pore-scale model including grains of the clastics is defined. An NMR response is simulated using the pore-scale model. A parameter of the pore-scale model is adjusted using the simulated response and the NMR signals. The simulated NMR response may include an NMR relaxation time spectrum and adjusting the parameter may be based on deriving a magnetization relaxation spectrum from the NMR signals and using the difference between the NMR relaxation time spectrum and the magnetization relaxation spectrum. The magnetization relaxation spectrum may be derived for a wetting phase that may be oil or water. The parameter being adjusted may be the grain size in the pore-scale model. The simulated NMR relaxation time spectrum may be obtained using a saturation of the wetting phase. Simulations may be made for imbibition or drainage. The difference may be reduced using a least-squares minimization. The pore scale model with the adjusted parameter may be used to simulate an additional property of the earth formation. The additional property may be a permeability, formation factor, and/or a surface to volume probability distribution.
The present disclosure is a significant extension of the teachings of Georgi et al. in that the pore-scale model is determined by using more than one type of measurements. By selection of the types of measurements, it is possible to estimate additional parameters of the pore-scale model. Moreover, the present disclosure broadens the application of the methodology. It shows that it is possible to estimate grain size distribution of the earth formation from downhole logging measurements (specifically, NMR relaxation time spectrum and acoustic velocities). Although pore-scale modeling concept is used in the teaching to illustrate the dependence, it is not necessary for the application of the methodology.